Solve by Graphing 2x-3y=2 x+2y=8

$2 x - 3 y = 2$ $x + 2 y = 8$

Step 1

Subtract $2 x$ from both sides of the equation.

$- 3 y = 2 - 2 x$

$x + 2 y = 8$

Step 2

Divide each term in $- 3 y = 2 - 2 x$ by $- 3$ and simplify.

Divide each term in $- 3 y = 2 - 2 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{2}{- 3} + \frac{- 2 x}{- 3}$

$x + 2 y = 8$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{2}{- 3} + \frac{- 2 x}{- 3}$

$x + 2 y = 8$

Divide $y$ by $1$ .

$y = \frac{2}{- 3} + \frac{- 2 x}{- 3}$

$x + 2 y = 8$

$y = \frac{2}{- 3} + \frac{- 2 x}{- 3}$

$x + 2 y = 8$

$y = \frac{2}{- 3} + \frac{- 2 x}{- 3}$

$x + 2 y = 8$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{2}{3} + \frac{- 2 x}{- 3}$

$x + 2 y = 8$

Dividing two negative values results in a positive value.

$y = - \frac{2}{3} + \frac{2 x}{3}$

$x + 2 y = 8$

$y = - \frac{2}{3} + \frac{2 x}{3}$

$x + 2 y = 8$

$y = - \frac{2}{3} + \frac{2 x}{3}$

$x + 2 y = 8$

$y = - \frac{2}{3} + \frac{2 x}{3}$

$x + 2 y = 8$

Step 3

Subtract $x$ from both sides of the equation.

$2 y = 8 - x$

$y = - \frac{2}{3} + \frac{2 x}{3}$

Step 4

Divide each term in $2 y = 8 - x$ by $2$ and simplify.

Divide each term in $2 y = 8 - x$ by $2$ .

$\frac{2 y}{2} = \frac{8}{2} + \frac{- x}{2}$

$y = - \frac{2}{3} + \frac{2 x}{3}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{8}{2} + \frac{- x}{2}$

$y = - \frac{2}{3} + \frac{2 x}{3}$

Divide $y$ by $1$ .

$y = \frac{8}{2} + \frac{- x}{2}$

$y = - \frac{2}{3} + \frac{2 x}{3}$

$y = \frac{8}{2} + \frac{- x}{2}$

$y = - \frac{2}{3} + \frac{2 x}{3}$

$y = \frac{8}{2} + \frac{- x}{2}$

$y = - \frac{2}{3} + \frac{2 x}{3}$

Simplify the right side.

Simplify each term.

Divide $8$ by $2$ .

$y = 4 + \frac{- x}{2}$

$y = - \frac{2}{3} + \frac{2 x}{3}$

Move the negative in front of the fraction.

$y = 4 - \frac{x}{2}$

$y = - \frac{2}{3} + \frac{2 x}{3}$

$y = 4 - \frac{x}{2}$

$y = - \frac{2}{3} + \frac{2 x}{3}$

$y = 4 - \frac{x}{2}$

$y = - \frac{2}{3} + \frac{2 x}{3}$

$y = 4 - \frac{x}{2}$

$y = - \frac{2}{3} + \frac{2 x}{3}$

Step 5

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

$(4, 2)$

Step 6

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